LMFDB - Embedded newform 8022.2.a.r.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8022,2,Mod(1,8022)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8022, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8022 = 2 \cdot 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8022.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0559925015$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 19x^{8} + 28x^{7} + 114x^{6} - 110x^{5} - 282x^{4} + 149x^{3} + 285x^{2} - 49x - 79 $ x^10 - 2x^9 - 19x^8 + 28x^7 + 114x^6 - 110x^5 - 282x^4 + 149x^3 + 285x^2 - 49*x - 79
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.667588$ of defining polynomial
Character	$\chi$	$=$	8022.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.332412 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.332412 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.332412 q^{10} +0.0285928 q^{11} -1.00000 q^{12} -6.71179 q^{13} +1.00000 q^{14} -0.332412 q^{15} +1.00000 q^{16} +3.25767 q^{17} +1.00000 q^{18} +1.72858 q^{19} +0.332412 q^{20} -1.00000 q^{21} +0.0285928 q^{22} +0.0708508 q^{23} -1.00000 q^{24} -4.88950 q^{25} -6.71179 q^{26} -1.00000 q^{27} +1.00000 q^{28} +0.0993871 q^{29} -0.332412 q^{30} +2.85299 q^{31} +1.00000 q^{32} -0.0285928 q^{33} +3.25767 q^{34} +0.332412 q^{35} +1.00000 q^{36} +8.64185 q^{37} +1.72858 q^{38} +6.71179 q^{39} +0.332412 q^{40} +0.999152 q^{41} -1.00000 q^{42} -3.82024 q^{43} +0.0285928 q^{44} +0.332412 q^{45} +0.0708508 q^{46} +3.20066 q^{47} -1.00000 q^{48} +1.00000 q^{49} -4.88950 q^{50} -3.25767 q^{51} -6.71179 q^{52} -3.45994 q^{53} -1.00000 q^{54} +0.00950458 q^{55} +1.00000 q^{56} -1.72858 q^{57} +0.0993871 q^{58} +5.89003 q^{59} -0.332412 q^{60} +7.83638 q^{61} +2.85299 q^{62} +1.00000 q^{63} +1.00000 q^{64} -2.23108 q^{65} -0.0285928 q^{66} -0.0586398 q^{67} +3.25767 q^{68} -0.0708508 q^{69} +0.332412 q^{70} -11.2652 q^{71} +1.00000 q^{72} +12.8636 q^{73} +8.64185 q^{74} +4.88950 q^{75} +1.72858 q^{76} +0.0285928 q^{77} +6.71179 q^{78} +4.61799 q^{79} +0.332412 q^{80} +1.00000 q^{81} +0.999152 q^{82} -16.2076 q^{83} -1.00000 q^{84} +1.08289 q^{85} -3.82024 q^{86} -0.0993871 q^{87} +0.0285928 q^{88} +16.0736 q^{89} +0.332412 q^{90} -6.71179 q^{91} +0.0708508 q^{92} -2.85299 q^{93} +3.20066 q^{94} +0.574600 q^{95} -1.00000 q^{96} +12.9496 q^{97} +1.00000 q^{98} +0.0285928 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} - 10 q^{3} + 10 q^{4} + 8 q^{5} - 10 q^{6} + 10 q^{7} + 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 - 10 * q^3 + 10 * q^4 + 8 * q^5 - 10 * q^6 + 10 * q^7 + 10 * q^8 + 10 * q^9	\( 10 q + 10 q^{2} - 10 q^{3} + 10 q^{4} + 8 q^{5} - 10 q^{6} + 10 q^{7} + 10 q^{8} + 10 q^{9} + 8 q^{10} + 4 q^{11} - 10 q^{12} + 6 q^{13} + 10 q^{14} - 8 q^{15} + 10 q^{16} + 5 q^{17} + 10 q^{18} + 15 q^{19} + 8 q^{20} - 10 q^{21} + 4 q^{22} + 12 q^{23} - 10 q^{24} - 2 q^{25} + 6 q^{26} - 10 q^{27} + 10 q^{28} + 7 q^{29} - 8 q^{30} + 28 q^{31} + 10 q^{32} - 4 q^{33} + 5 q^{34} + 8 q^{35} + 10 q^{36} - 3 q^{37} + 15 q^{38} - 6 q^{39} + 8 q^{40} + 24 q^{41} - 10 q^{42} + 4 q^{43} + 4 q^{44} + 8 q^{45} + 12 q^{46} + 16 q^{47} - 10 q^{48} + 10 q^{49} - 2 q^{50} - 5 q^{51} + 6 q^{52} + 5 q^{53} - 10 q^{54} - q^{55} + 10 q^{56} - 15 q^{57} + 7 q^{58} + 17 q^{59} - 8 q^{60} + 15 q^{61} + 28 q^{62} + 10 q^{63} + 10 q^{64} + 14 q^{65} - 4 q^{66} + 6 q^{67} + 5 q^{68} - 12 q^{69} + 8 q^{70} + 5 q^{71} + 10 q^{72} + 16 q^{73} - 3 q^{74} + 2 q^{75} + 15 q^{76} + 4 q^{77} - 6 q^{78} - 5 q^{79} + 8 q^{80} + 10 q^{81} + 24 q^{82} + 24 q^{83} - 10 q^{84} - 19 q^{85} + 4 q^{86} - 7 q^{87} + 4 q^{88} + 17 q^{89} + 8 q^{90} + 6 q^{91} + 12 q^{92} - 28 q^{93} + 16 q^{94} + 15 q^{95} - 10 q^{96} + 20 q^{97} + 10 q^{98} + 4 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 - 10 * q^3 + 10 * q^4 + 8 * q^5 - 10 * q^6 + 10 * q^7 + 10 * q^8 + 10 * q^9 + 8 * q^10 + 4 * q^11 - 10 * q^12 + 6 * q^13 + 10 * q^14 - 8 * q^15 + 10 * q^16 + 5 * q^17 + 10 * q^18 + 15 * q^19 + 8 * q^20 - 10 * q^21 + 4 * q^22 + 12 * q^23 - 10 * q^24 - 2 * q^25 + 6 * q^26 - 10 * q^27 + 10 * q^28 + 7 * q^29 - 8 * q^30 + 28 * q^31 + 10 * q^32 - 4 * q^33 + 5 * q^34 + 8 * q^35 + 10 * q^36 - 3 * q^37 + 15 * q^38 - 6 * q^39 + 8 * q^40 + 24 * q^41 - 10 * q^42 + 4 * q^43 + 4 * q^44 + 8 * q^45 + 12 * q^46 + 16 * q^47 - 10 * q^48 + 10 * q^49 - 2 * q^50 - 5 * q^51 + 6 * q^52 + 5 * q^53 - 10 * q^54 - q^55 + 10 * q^56 - 15 * q^57 + 7 * q^58 + 17 * q^59 - 8 * q^60 + 15 * q^61 + 28 * q^62 + 10 * q^63 + 10 * q^64 + 14 * q^65 - 4 * q^66 + 6 * q^67 + 5 * q^68 - 12 * q^69 + 8 * q^70 + 5 * q^71 + 10 * q^72 + 16 * q^73 - 3 * q^74 + 2 * q^75 + 15 * q^76 + 4 * q^77 - 6 * q^78 - 5 * q^79 + 8 * q^80 + 10 * q^81 + 24 * q^82 + 24 * q^83 - 10 * q^84 - 19 * q^85 + 4 * q^86 - 7 * q^87 + 4 * q^88 + 17 * q^89 + 8 * q^90 + 6 * q^91 + 12 * q^92 - 28 * q^93 + 16 * q^94 + 15 * q^95 - 10 * q^96 + 20 * q^97 + 10 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	0.332412	0.148659	0.0743295	−	0.997234i	$-0.476318\pi$
$5$	0.332412	0.148659	0.0743295	+	0.997234i	$0.476318\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.332412	0.105118
$11$	0.0285928	0.00862105	0.00431053	−	0.999991i	$-0.498628\pi$
$11$	0.0285928	0.00862105	0.00431053	+	0.999991i	$0.498628\pi$
$12$	−1.00000	−0.288675
$13$	−6.71179	−1.86152	−0.930758	−	0.365635i	$-0.880852\pi$
$13$	−6.71179	−1.86152	−0.930758	+	0.365635i	$0.880852\pi$
$14$	1.00000	0.267261
$15$	−0.332412	−0.0858283
$16$	1.00000	0.250000
$17$	3.25767	0.790102	0.395051	−	0.918659i	$-0.370727\pi$
$17$	3.25767	0.790102	0.395051	+	0.918659i	$0.370727\pi$
$18$	1.00000	0.235702
$19$	1.72858	0.396564	0.198282	−	0.980145i	$-0.436464\pi$
$19$	1.72858	0.396564	0.198282	+	0.980145i	$0.436464\pi$
$20$	0.332412	0.0743295
$21$	−1.00000	−0.218218
$22$	0.0285928	0.00609601
$23$	0.0708508	0.0147734	0.00738670	−	0.999973i	$-0.497649\pi$
$23$	0.0708508	0.0147734	0.00738670	+	0.999973i	$0.497649\pi$
$24$	−1.00000	−0.204124
$25$	−4.88950	−0.977901
$26$	−6.71179	−1.31629
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	0.0993871	0.0184557	0.00922786	−	0.999957i	$-0.497063\pi$
$29$	0.0993871	0.0184557	0.00922786	+	0.999957i	$0.497063\pi$
$30$	−0.332412	−0.0606898
$31$	2.85299	0.512412	0.256206	−	0.966622i	$-0.417527\pi$
$31$	2.85299	0.512412	0.256206	+	0.966622i	$0.417527\pi$
$32$	1.00000	0.176777
$33$	−0.0285928	−0.00497737
$34$	3.25767	0.558686
$35$	0.332412	0.0561878
$36$	1.00000	0.166667
$37$	8.64185	1.42071	0.710356	−	0.703843i	$-0.248534\pi$
$37$	8.64185	1.42071	0.710356	+	0.703843i	$0.248534\pi$
$38$	1.72858	0.280413
$39$	6.71179	1.07475
$40$	0.332412	0.0525589
$41$	0.999152	0.156041	0.0780207	−	0.996952i	$-0.475140\pi$
$41$	0.999152	0.156041	0.0780207	+	0.996952i	$0.475140\pi$
$42$	−1.00000	−0.154303
$43$	−3.82024	−0.582582	−0.291291	−	0.956635i	$-0.594085\pi$
$43$	−3.82024	−0.582582	−0.291291	+	0.956635i	$0.594085\pi$
$44$	0.0285928	0.00431053
$45$	0.332412	0.0495530
$46$	0.0708508	0.0104464
$47$	3.20066	0.466864	0.233432	−	0.972373i	$-0.425004\pi$
$47$	3.20066	0.466864	0.233432	+	0.972373i	$0.425004\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−4.88950	−0.691480
$51$	−3.25767	−0.456165
$52$	−6.71179	−0.930758
$53$	−3.45994	−0.475259	−0.237629	−	0.971356i	$-0.576370\pi$
$53$	−3.45994	−0.475259	−0.237629	+	0.971356i	$0.576370\pi$
$54$	−1.00000	−0.136083
$55$	0.00950458	0.00128160
$56$	1.00000	0.133631
$57$	−1.72858	−0.228956
$58$	0.0993871	0.0130502
$59$	5.89003	0.766817	0.383408	−	0.923579i	$-0.374750\pi$
$59$	5.89003	0.766817	0.383408	+	0.923579i	$0.374750\pi$
$60$	−0.332412	−0.0429141
$61$	7.83638	1.00335	0.501673	−	0.865057i	$-0.332718\pi$
$61$	7.83638	1.00335	0.501673	+	0.865057i	$0.332718\pi$
$62$	2.85299	0.362330
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	−2.23108	−0.276731
$66$	−0.0285928	−0.00351953
$67$	−0.0586398	−0.00716399	−0.00358200	−	0.999994i	$-0.501140\pi$
$67$	−0.0586398	−0.00716399	−0.00358200	+	0.999994i	$0.501140\pi$
$68$	3.25767	0.395051
$69$	−0.0708508	−0.00852943
$70$	0.332412	0.0397308
$71$	−11.2652	−1.33694	−0.668468	−	0.743741i	$-0.733050\pi$
$71$	−11.2652	−1.33694	−0.668468	+	0.743741i	$0.733050\pi$
$72$	1.00000	0.117851
$73$	12.8636	1.50557	0.752784	−	0.658268i	$-0.228711\pi$
$73$	12.8636	1.50557	0.752784	+	0.658268i	$0.228711\pi$
$74$	8.64185	1.00459
$75$	4.88950	0.564591
$76$	1.72858	0.198282
$77$	0.0285928	0.00325845
$78$	6.71179	0.759961
$79$	4.61799	0.519564	0.259782	−	0.965667i	$-0.416349\pi$
$79$	4.61799	0.519564	0.259782	+	0.965667i	$0.416349\pi$
$80$	0.332412	0.0371647
$81$	1.00000	0.111111
$82$	0.999152	0.110338
$83$	−16.2076	−1.77901	−0.889507	−	0.456922i	$-0.848952\pi$
$83$	−16.2076	−1.77901	−0.889507	+	0.456922i	$0.848952\pi$
$84$	−1.00000	−0.109109
$85$	1.08289	0.117456
$86$	−3.82024	−0.411947
$87$	−0.0993871	−0.0106554
$88$	0.0285928	0.00304800
$89$	16.0736	1.70380	0.851899	−	0.523707i	$-0.175451\pi$
$89$	16.0736	1.70380	0.851899	+	0.523707i	$0.175451\pi$
$90$	0.332412	0.0350393
$91$	−6.71179	−0.703587
$92$	0.0708508	0.00738670
$93$	−2.85299	−0.295841
$94$	3.20066	0.330122
$95$	0.574600	0.0589527
$96$	−1.00000	−0.102062
$97$	12.9496	1.31483	0.657417	−	0.753527i	$-0.271649\pi$
$97$	12.9496	1.31483	0.657417	+	0.753527i	$0.271649\pi$
$98$	1.00000	0.101015
$99$	0.0285928	0.00287368
$100$	−4.88950	−0.488950
$101$	2.25647	0.224527	0.112263	−	0.993678i	$-0.464190\pi$
$101$	2.25647	0.224527	0.112263	+	0.993678i	$0.464190\pi$
$102$	−3.25767	−0.322558
$103$	18.4861	1.82149	0.910747	−	0.412965i	$-0.135507\pi$
$103$	18.4861	1.82149	0.910747	+	0.412965i	$0.135507\pi$
$104$	−6.71179	−0.658146
$105$	−0.332412	−0.0324400
$106$	−3.45994	−0.336059
$107$	13.7691	1.33111	0.665555	−	0.746348i	$-0.268195\pi$
$107$	13.7691	1.33111	0.665555	+	0.746348i	$0.268195\pi$
$108$	−1.00000	−0.0962250
$109$	−5.87807	−0.563017	−0.281508	−	0.959559i	$-0.590835\pi$
$109$	−5.87807	−0.563017	−0.281508	+	0.959559i	$0.590835\pi$
$110$	0.00950458	0.000906226 0
$111$	−8.64185	−0.820248
$112$	1.00000	0.0944911
$113$	−2.59872	−0.244467	−0.122233	−	0.992501i	$-0.539006\pi$
$113$	−2.59872	−0.244467	−0.122233	+	0.992501i	$0.539006\pi$
$114$	−1.72858	−0.161896
$115$	0.0235516	0.00219620
$116$	0.0993871	0.00922786
$117$	−6.71179	−0.620506
$118$	5.89003	0.542221
$119$	3.25767	0.298630
$120$	−0.332412	−0.0303449
$121$	−10.9992	−0.999926
$122$	7.83638	0.709473
$123$	−0.999152	−0.0900905
$124$	2.85299	0.256206
$125$	−3.28739	−0.294033
$126$	1.00000	0.0890871
$127$	13.8473	1.22875	0.614376	−	0.789014i	$-0.289408\pi$
$127$	13.8473	1.22875	0.614376	+	0.789014i	$0.289408\pi$
$128$	1.00000	0.0883883
$129$	3.82024	0.336354
$130$	−2.23108	−0.195679
$131$	9.67996	0.845742	0.422871	−	0.906190i	$-0.361022\pi$
$131$	9.67996	0.845742	0.422871	+	0.906190i	$0.361022\pi$
$132$	−0.0285928	−0.00248868
$133$	1.72858	0.149887
$134$	−0.0586398	−0.00506571
$135$	−0.332412	−0.0286094
$136$	3.25767	0.279343
$137$	−2.87652	−0.245758	−0.122879	−	0.992422i	$-0.539213\pi$
$137$	−2.87652	−0.245758	−0.122879	+	0.992422i	$0.539213\pi$
$138$	−0.0708508	−0.00603122
$139$	13.4317	1.13926	0.569630	−	0.821901i	$-0.307086\pi$
$139$	13.4317	1.13926	0.569630	+	0.821901i	$0.307086\pi$
$140$	0.332412	0.0280939
$141$	−3.20066	−0.269544
$142$	−11.2652	−0.945357
$143$	−0.191909	−0.0160482
$144$	1.00000	0.0833333
$145$	0.0330374	0.00274361
$146$	12.8636	1.06460
$147$	−1.00000	−0.0824786
$148$	8.64185	0.710356
$149$	0.853602	0.0699298	0.0349649	−	0.999389i	$-0.488868\pi$
$149$	0.853602	0.0699298	0.0349649	+	0.999389i	$0.488868\pi$
$150$	4.88950	0.399226
$151$	1.26304	0.102785	0.0513923	−	0.998679i	$-0.483634\pi$
$151$	1.26304	0.102785	0.0513923	+	0.998679i	$0.483634\pi$
$152$	1.72858	0.140206
$153$	3.25767	0.263367
$154$	0.0285928	0.00230407
$155$	0.948367	0.0761747
$156$	6.71179	0.537374
$157$	−8.32618	−0.664502	−0.332251	−	0.943191i	$-0.607808\pi$
$157$	−8.32618	−0.664502	−0.332251	+	0.943191i	$0.607808\pi$
$158$	4.61799	0.367388
$159$	3.45994	0.274391
$160$	0.332412	0.0262794
$161$	0.0708508	0.00558382
$162$	1.00000	0.0785674
$163$	−1.32359	−0.103672	−0.0518359	−	0.998656i	$-0.516507\pi$
$163$	−1.32359	−0.103672	−0.0518359	+	0.998656i	$0.516507\pi$
$164$	0.999152	0.0780207
$165$	−0.00950458	−0.000739930 0
$166$	−16.2076	−1.25795
$167$	6.48446	0.501782	0.250891	−	0.968015i	$-0.419276\pi$
$167$	6.48446	0.501782	0.250891	+	0.968015i	$0.419276\pi$
$168$	−1.00000	−0.0771517
$169$	32.0482	2.46525
$170$	1.08289	0.0830537
$171$	1.72858	0.132188
$172$	−3.82024	−0.291291
$173$	−0.314802	−0.0239339	−0.0119670	−	0.999928i	$-0.503809\pi$
$173$	−0.314802	−0.0239339	−0.0119670	+	0.999928i	$0.503809\pi$
$174$	−0.0993871	−0.00753451
$175$	−4.88950	−0.369612
$176$	0.0285928	0.00215526
$177$	−5.89003	−0.442722
$178$	16.0736	1.20477
$179$	−25.0999	−1.87605	−0.938026	−	0.346565i	$-0.887348\pi$
$179$	−25.0999	−1.87605	−0.938026	+	0.346565i	$0.887348\pi$
$180$	0.332412	0.0247765
$181$	−9.03742	−0.671746	−0.335873	−	0.941907i	$-0.609031\pi$
$181$	−9.03742	−0.671746	−0.335873	+	0.941907i	$0.609031\pi$
$182$	−6.71179	−0.497511
$183$	−7.83638	−0.579282
$184$	0.0708508	0.00522319
$185$	2.87265	0.211201
$186$	−2.85299	−0.209192
$187$	0.0931460	0.00681151
$188$	3.20066	0.233432
$189$	−1.00000	−0.0727393
$190$	0.574600	0.0416859
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	−1.00000	−0.0721688
$193$	−12.2412	−0.881141	−0.440570	−	0.897718i	$-0.645224\pi$
$193$	−12.2412	−0.881141	−0.440570	+	0.897718i	$0.645224\pi$
$194$	12.9496	0.929728
$195$	2.23108	0.159771
$196$	1.00000	0.0714286
$197$	17.6606	1.25826	0.629132	−	0.777298i	$-0.283410\pi$
$197$	17.6606	1.25826	0.629132	+	0.777298i	$0.283410\pi$
$198$	0.0285928	0.00203200
$199$	1.97046	0.139682	0.0698409	−	0.997558i	$-0.477751\pi$
$199$	1.97046	0.139682	0.0698409	+	0.997558i	$0.477751\pi$
$200$	−4.88950	−0.345740
$201$	0.0586398	0.00413613
$202$	2.25647	0.158765
$203$	0.0993871	0.00697560
$204$	−3.25767	−0.228083
$205$	0.332130	0.0231970
$206$	18.4861	1.28799
$207$	0.0708508	0.00492447
$208$	−6.71179	−0.465379
$209$	0.0494250	0.00341880
$210$	−0.332412	−0.0229386
$211$	−25.3536	−1.74541	−0.872706	−	0.488247i	$-0.837637\pi$
$211$	−25.3536	−1.74541	−0.872706	+	0.488247i	$0.837637\pi$
$212$	−3.45994	−0.237629
$213$	11.2652	0.771880
$214$	13.7691	0.941238
$215$	−1.26989	−0.0866060
$216$	−1.00000	−0.0680414
$217$	2.85299	0.193674
$218$	−5.87807	−0.398113
$219$	−12.8636	−0.869240
$220$	0.00950458	0.000640799 0
$221$	−21.8648	−1.47079
$222$	−8.64185	−0.580003
$223$	−1.68373	−0.112751	−0.0563753	−	0.998410i	$-0.517954\pi$
$223$	−1.68373	−0.112751	−0.0563753	+	0.998410i	$0.517954\pi$
$224$	1.00000	0.0668153
$225$	−4.88950	−0.325967
$226$	−2.59872	−0.172864
$227$	−7.47432	−0.496088	−0.248044	−	0.968749i	$-0.579788\pi$
$227$	−7.47432	−0.496088	−0.248044	+	0.968749i	$0.579788\pi$
$228$	−1.72858	−0.114478
$229$	10.3911	0.686666	0.343333	−	0.939214i	$-0.388444\pi$
$229$	10.3911	0.686666	0.343333	+	0.939214i	$0.388444\pi$
$230$	0.0235516	0.00155295
$231$	−0.0285928	−0.00188127
$232$	0.0993871	0.00652508
$233$	16.1566	1.05846	0.529228	−	0.848480i	$-0.322482\pi$
$233$	16.1566	1.05846	0.529228	+	0.848480i	$0.322482\pi$
$234$	−6.71179	−0.438764
$235$	1.06394	0.0694035
$236$	5.89003	0.383408
$237$	−4.61799	−0.299971
$238$	3.25767	0.211164
$239$	−5.75416	−0.372205	−0.186103	−	0.982530i	$-0.559586\pi$
$239$	−5.75416	−0.372205	−0.186103	+	0.982530i	$0.559586\pi$
$240$	−0.332412	−0.0214571
$241$	8.77669	0.565356	0.282678	−	0.959215i	$-0.408777\pi$
$241$	8.77669	0.565356	0.282678	+	0.959215i	$0.408777\pi$
$242$	−10.9992	−0.707054
$243$	−1.00000	−0.0641500
$244$	7.83638	0.501673
$245$	0.332412	0.0212370
$246$	−0.999152	−0.0637036
$247$	−11.6019	−0.738210
$248$	2.85299	0.181165
$249$	16.2076	1.02711
$250$	−3.28739	−0.207912
$251$	−1.70378	−0.107542	−0.0537710	−	0.998553i	$-0.517124\pi$
$251$	−1.70378	−0.107542	−0.0537710	+	0.998553i	$0.517124\pi$
$252$	1.00000	0.0629941
$253$	0.00202582	0.000127362 0
$254$	13.8473	0.868859
$255$	−1.08289	−0.0678131
$256$	1.00000	0.0625000
$257$	−0.400063	−0.0249553	−0.0124776	−	0.999922i	$-0.503972\pi$
$257$	−0.400063	−0.0249553	−0.0124776	+	0.999922i	$0.503972\pi$
$258$	3.82024	0.237838
$259$	8.64185	0.536978
$260$	−2.23108	−0.138366
$261$	0.0993871	0.00615191
$262$	9.67996	0.598030
$263$	5.86895	0.361895	0.180947	−	0.983493i	$-0.442084\pi$
$263$	5.86895	0.361895	0.180947	+	0.983493i	$0.442084\pi$
$264$	−0.0285928	−0.00175977
$265$	−1.15012	−0.0706515
$266$	1.72858	0.105986
$267$	−16.0736	−0.983688
$268$	−0.0586398	−0.00358200
$269$	−1.35497	−0.0826141	−0.0413070	−	0.999146i	$-0.513152\pi$
$269$	−1.35497	−0.0826141	−0.0413070	+	0.999146i	$0.513152\pi$
$270$	−0.332412	−0.0202299
$271$	−18.8911	−1.14755	−0.573776	−	0.819012i	$-0.694522\pi$
$271$	−18.8911	−1.14755	−0.573776	+	0.819012i	$0.694522\pi$
$272$	3.25767	0.197525
$273$	6.71179	0.406216
$274$	−2.87652	−0.173777
$275$	−0.139805	−0.00843053
$276$	−0.0708508	−0.00426471
$277$	15.3467	0.922094	0.461047	−	0.887376i	$-0.347474\pi$
$277$	15.3467	0.922094	0.461047	+	0.887376i	$0.347474\pi$
$278$	13.4317	0.805579
$279$	2.85299	0.170804
$280$	0.332412	0.0198654
$281$	18.2141	1.08656	0.543281	−	0.839551i	$-0.317182\pi$
$281$	18.2141	1.08656	0.543281	+	0.839551i	$0.317182\pi$
$282$	−3.20066	−0.190596
$283$	23.9737	1.42509	0.712544	−	0.701628i	$-0.247543\pi$
$283$	23.9737	1.42509	0.712544	+	0.701628i	$0.247543\pi$
$284$	−11.2652	−0.668468
$285$	−0.574600	−0.0340364
$286$	−0.191909	−0.0113478
$287$	0.999152	0.0589781
$288$	1.00000	0.0589256
$289$	−6.38757	−0.375739
$290$	0.0330374	0.00194002
$291$	−12.9496	−0.759120
$292$	12.8636	0.752784
$293$	23.5020	1.37300	0.686501	−	0.727129i	$-0.259146\pi$
$293$	23.5020	1.37300	0.686501	+	0.727129i	$0.259146\pi$
$294$	−1.00000	−0.0583212
$295$	1.95791	0.113994
$296$	8.64185	0.502297
$297$	−0.0285928	−0.00165912
$298$	0.853602	0.0494478
$299$	−0.475536	−0.0275009
$300$	4.88950	0.282296
$301$	−3.82024	−0.220195
$302$	1.26304	0.0726797
$303$	−2.25647	−0.129631
$304$	1.72858	0.0991409
$305$	2.60490	0.149156
$306$	3.25767	0.186229
$307$	−14.2852	−0.815298	−0.407649	−	0.913139i	$-0.633651\pi$
$307$	−14.2852	−0.815298	−0.407649	+	0.913139i	$0.633651\pi$
$308$	0.0285928	0.00162923
$309$	−18.4861	−1.05164
$310$	0.948367	0.0538637
$311$	21.0368	1.19289	0.596444	−	0.802655i	$-0.296580\pi$
$311$	21.0368	1.19289	0.596444	+	0.802655i	$0.296580\pi$
$312$	6.71179	0.379981
$313$	−13.3859	−0.756615	−0.378308	−	0.925680i	$-0.623494\pi$
$313$	−13.3859	−0.756615	−0.378308	+	0.925680i	$0.623494\pi$
$314$	−8.32618	−0.469874
$315$	0.332412	0.0187293
$316$	4.61799	0.259782
$317$	16.9767	0.953505	0.476752	−	0.879038i	$-0.341814\pi$
$317$	16.9767	0.953505	0.476752	+	0.879038i	$0.341814\pi$
$318$	3.45994	0.194024
$319$	0.00284175	0.000159108 0
$320$	0.332412	0.0185824
$321$	−13.7691	−0.768517
$322$	0.0708508	0.00394836
$323$	5.63115	0.313325
$324$	1.00000	0.0555556
$325$	32.8173	1.82038
$326$	−1.32359	−0.0733071
$327$	5.87807	0.325058
$328$	0.999152	0.0551690
$329$	3.20066	0.176458
$330$	−0.00950458	−0.000523210 0
$331$	31.3477	1.72302	0.861512	−	0.507737i	$-0.169518\pi$
$331$	31.3477	1.72302	0.861512	+	0.507737i	$0.169518\pi$
$332$	−16.2076	−0.889507
$333$	8.64185	0.473570
$334$	6.48446	0.354814
$335$	−0.0194925	−0.00106499
$336$	−1.00000	−0.0545545
$337$	−17.3575	−0.945525	−0.472762	−	0.881190i	$-0.656743\pi$
$337$	−17.3575	−0.945525	−0.472762	+	0.881190i	$0.656743\pi$
$338$	32.0482	1.74319
$339$	2.59872	0.141143
$340$	1.08289	0.0587278
$341$	0.0815750	0.00441754
$342$	1.72858	0.0934709
$343$	1.00000	0.0539949
$344$	−3.82024	−0.205974
$345$	−0.0235516	−0.00126798
$346$	−0.314802	−0.0169239
$347$	26.6171	1.42888	0.714441	−	0.699695i	$-0.246681\pi$
$347$	26.6171	1.42888	0.714441	+	0.699695i	$0.246681\pi$
$348$	−0.0993871	−0.00532771
$349$	−22.5782	−1.20858	−0.604291	−	0.796763i	$-0.706544\pi$
$349$	−22.5782	−1.20858	−0.604291	+	0.796763i	$0.706544\pi$
$350$	−4.88950	−0.261355
$351$	6.71179	0.358249
$352$	0.0285928	0.00152400
$353$	0.854762	0.0454944	0.0227472	−	0.999741i	$-0.492759\pi$
$353$	0.854762	0.0454944	0.0227472	+	0.999741i	$0.492759\pi$
$354$	−5.89003	−0.313052
$355$	−3.74469	−0.198748
$356$	16.0736	0.851899
$357$	−3.25767	−0.172414
$358$	−25.0999	−1.32657
$359$	15.4986	0.817982	0.408991	−	0.912538i	$-0.365881\pi$
$359$	15.4986	0.817982	0.408991	+	0.912538i	$0.365881\pi$
$360$	0.332412	0.0175196
$361$	−16.0120	−0.842737
$362$	−9.03742	−0.474996
$363$	10.9992	0.577307
$364$	−6.71179	−0.351794
$365$	4.27600	0.223816
$366$	−7.83638	−0.409614
$367$	24.6641	1.28746	0.643728	−	0.765255i	$-0.277387\pi$
$367$	24.6641	1.28746	0.643728	+	0.765255i	$0.277387\pi$
$368$	0.0708508	0.00369335
$369$	0.999152	0.0520138
$370$	2.87265	0.149342
$371$	−3.45994	−0.179631
$372$	−2.85299	−0.147921
$373$	−19.5924	−1.01446	−0.507228	−	0.861812i	$-0.669330\pi$
$373$	−19.5924	−1.01446	−0.507228	+	0.861812i	$0.669330\pi$
$374$	0.0931460	0.00481646
$375$	3.28739	0.169760
$376$	3.20066	0.165061
$377$	−0.667066	−0.0343556
$378$	−1.00000	−0.0514344
$379$	9.25494	0.475394	0.237697	−	0.971339i	$-0.423607\pi$
$379$	9.25494	0.475394	0.237697	+	0.971339i	$0.423607\pi$
$380$	0.574600	0.0294764
$381$	−13.8473	−0.709420
$382$	1.00000	0.0511645
$383$	−11.8444	−0.605221	−0.302610	−	0.953114i	$-0.597858\pi$
$383$	−11.8444	−0.605221	−0.302610	+	0.953114i	$0.597858\pi$
$384$	−1.00000	−0.0510310
$385$	0.00950458	0.000484398 0
$386$	−12.2412	−0.623061
$387$	−3.82024	−0.194194
$388$	12.9496	0.657417
$389$	4.22403	0.214167	0.107084	−	0.994250i	$-0.465849\pi$
$389$	4.22403	0.214167	0.107084	+	0.994250i	$0.465849\pi$
$390$	2.23108	0.112975
$391$	0.230809	0.0116725
$392$	1.00000	0.0505076
$393$	−9.67996	−0.488290
$394$	17.6606	0.889727
$395$	1.53507	0.0772379
$396$	0.0285928	0.00143684
$397$	30.1111	1.51124	0.755618	−	0.655013i	$-0.227337\pi$
$397$	30.1111	1.51124	0.755618	+	0.655013i	$0.227337\pi$
$398$	1.97046	0.0987700
$399$	−1.72858	−0.0865373
$400$	−4.88950	−0.244475
$401$	5.72585	0.285935	0.142968	−	0.989727i	$-0.454336\pi$
$401$	5.72585	0.285935	0.142968	+	0.989727i	$0.454336\pi$
$402$	0.0586398	0.00292469
$403$	−19.1487	−0.953864
$404$	2.25647	0.112263
$405$	0.332412	0.0165177
$406$	0.0993871	0.00493250
$407$	0.247095	0.0122480
$408$	−3.25767	−0.161279
$409$	−14.8710	−0.735326	−0.367663	−	0.929959i	$-0.619842\pi$
$409$	−14.8710	−0.735326	−0.367663	+	0.929959i	$0.619842\pi$
$410$	0.332130	0.0164027
$411$	2.87652	0.141888
$412$	18.4861	0.910747
$413$	5.89003	0.289830
$414$	0.0708508	0.00348212
$415$	−5.38759	−0.264466
$416$	−6.71179	−0.329073
$417$	−13.4317	−0.657752
$418$	0.0494250	0.00241745
$419$	28.9697	1.41526	0.707632	−	0.706581i	$-0.249763\pi$
$419$	28.9697	1.41526	0.707632	+	0.706581i	$0.249763\pi$
$420$	−0.332412	−0.0162200
$421$	−5.98538	−0.291710	−0.145855	−	0.989306i	$-0.546593\pi$
$421$	−5.98538	−0.291710	−0.145855	+	0.989306i	$0.546593\pi$
$422$	−25.3536	−1.23419
$423$	3.20066	0.155621
$424$	−3.45994	−0.168029
$425$	−15.9284	−0.772641
$426$	11.2652	0.545802
$427$	7.83638	0.379229
$428$	13.7691	0.665555
$429$	0.191909	0.00926545
$430$	−1.26989	−0.0612397
$431$	28.8160	1.38802	0.694010	−	0.719966i	$-0.255842\pi$
$431$	28.8160	1.38802	0.694010	+	0.719966i	$0.255842\pi$
$432$	−1.00000	−0.0481125
$433$	−25.4284	−1.22201	−0.611006	−	0.791626i	$-0.709235\pi$
$433$	−25.4284	−1.22201	−0.611006	+	0.791626i	$0.709235\pi$
$434$	2.85299	0.136948
$435$	−0.0330374	−0.00158402
$436$	−5.87807	−0.281508
$437$	0.122471	0.00585859
$438$	−12.8636	−0.614645
$439$	−22.0601	−1.05287	−0.526435	−	0.850215i	$-0.676472\pi$
$439$	−22.0601	−1.05287	−0.526435	+	0.850215i	$0.676472\pi$
$440$	0.00950458	0.000453113 0
$441$	1.00000	0.0476190
$442$	−21.8648	−1.04000
$443$	13.5435	0.643473	0.321737	−	0.946829i	$-0.395733\pi$
$443$	13.5435	0.643473	0.321737	+	0.946829i	$0.395733\pi$
$444$	−8.64185	−0.410124
$445$	5.34305	0.253285
$446$	−1.68373	−0.0797267
$447$	−0.853602	−0.0403740
$448$	1.00000	0.0472456
$449$	32.1764	1.51850	0.759250	−	0.650799i	$-0.225566\pi$
$449$	32.1764	1.51850	0.759250	+	0.650799i	$0.225566\pi$
$450$	−4.88950	−0.230493
$451$	0.0285686	0.00134524
$452$	−2.59872	−0.122233
$453$	−1.26304	−0.0593427
$454$	−7.47432	−0.350787
$455$	−2.23108	−0.104595
$456$	−1.72858	−0.0809482
$457$	−36.9368	−1.72783	−0.863914	−	0.503639i	$-0.831994\pi$
$457$	−36.9368	−1.72783	−0.863914	+	0.503639i	$0.831994\pi$
$458$	10.3911	0.485546
$459$	−3.25767	−0.152055
$460$	0.0235516	0.00109810
$461$	−30.9432	−1.44117	−0.720585	−	0.693367i	$-0.756127\pi$
$461$	−30.9432	−1.44117	−0.720585	+	0.693367i	$0.756127\pi$
$462$	−0.0285928	−0.00133026
$463$	−15.4331	−0.717235	−0.358617	−	0.933485i	$-0.616752\pi$
$463$	−15.4331	−0.717235	−0.358617	+	0.933485i	$0.616752\pi$
$464$	0.0993871	0.00461393
$465$	−0.948367	−0.0439795
$466$	16.1566	0.748442
$467$	7.14773	0.330758	0.165379	−	0.986230i	$-0.447115\pi$
$467$	7.14773	0.330758	0.165379	+	0.986230i	$0.447115\pi$
$468$	−6.71179	−0.310253
$469$	−0.0586398	−0.00270773
$470$	1.06394	0.0490757
$471$	8.32618	0.383650
$472$	5.89003	0.271111
$473$	−0.109231	−0.00502247
$474$	−4.61799	−0.212111
$475$	−8.45190	−0.387800
$476$	3.25767	0.149315
$477$	−3.45994	−0.158420
$478$	−5.75416	−0.263189
$479$	22.1217	1.01076	0.505382	−	0.862896i	$-0.331351\pi$
$479$	22.1217	1.01076	0.505382	+	0.862896i	$0.331351\pi$
$480$	−0.332412	−0.0151724
$481$	−58.0023	−2.64468
$482$	8.77669	0.399767
$483$	−0.0708508	−0.00322382
$484$	−10.9992	−0.499963
$485$	4.30460	0.195462
$486$	−1.00000	−0.0453609
$487$	2.26919	0.102827	0.0514134	−	0.998677i	$-0.483627\pi$
$487$	2.26919	0.102827	0.0514134	+	0.998677i	$0.483627\pi$
$488$	7.83638	0.354736
$489$	1.32359	0.0598550
$490$	0.332412	0.0150168
$491$	−41.7450	−1.88392	−0.941962	−	0.335719i	$-0.891021\pi$
$491$	−41.7450	−1.88392	−0.941962	+	0.335719i	$0.891021\pi$
$492$	−0.999152	−0.0450453
$493$	0.323771	0.0145819
$494$	−11.6019	−0.521993
$495$	0.00950458	0.000427199 0
$496$	2.85299	0.128103
$497$	−11.2652	−0.505314
$498$	16.2076	0.726279
$499$	−0.872781	−0.0390710	−0.0195355	−	0.999809i	$-0.506219\pi$
$499$	−0.872781	−0.0390710	−0.0195355	+	0.999809i	$0.506219\pi$
$500$	−3.28739	−0.147016
$501$	−6.48446	−0.289704
$502$	−1.70378	−0.0760436
$503$	12.4453	0.554909	0.277455	−	0.960739i	$-0.410509\pi$
$503$	12.4453	0.554909	0.277455	+	0.960739i	$0.410509\pi$
$504$	1.00000	0.0445435
$505$	0.750076	0.0333779
$506$	0.00202582	9.00588e−5 0
$507$	−32.0482	−1.42331
$508$	13.8473	0.614376
$509$	−26.8160	−1.18860	−0.594299	−	0.804244i	$-0.702571\pi$
$509$	−26.8160	−1.18860	−0.594299	+	0.804244i	$0.702571\pi$
$510$	−1.08289	−0.0479511
$511$	12.8636	0.569051
$512$	1.00000	0.0441942
$513$	−1.72858	−0.0763187
$514$	−0.400063	−0.0176460
$515$	6.14501	0.270781
$516$	3.82024	0.168177
$517$	0.0915157	0.00402486
$518$	8.64185	0.379701
$519$	0.314802	0.0138183
$520$	−2.23108	−0.0978393
$521$	20.5287	0.899377	0.449688	−	0.893186i	$-0.351535\pi$
$521$	20.5287	0.899377	0.449688	+	0.893186i	$0.351535\pi$
$522$	0.0993871	0.00435005
$523$	38.1541	1.66836	0.834181	−	0.551491i	$-0.185941\pi$
$523$	38.1541	1.66836	0.834181	+	0.551491i	$0.185941\pi$
$524$	9.67996	0.422871
$525$	4.88950	0.213395
$526$	5.86895	0.255898
$527$	9.29411	0.404858
$528$	−0.0285928	−0.00124434
$529$	−22.9950	−0.999782
$530$	−1.15012	−0.0499581
$531$	5.89003	0.255606
$532$	1.72858	0.0749435
$533$	−6.70611	−0.290474
$534$	−16.0736	−0.695572
$535$	4.57701	0.197882
$536$	−0.0586398	−0.00253285
$537$	25.0999	1.08314
$538$	−1.35497	−0.0584170
$539$	0.0285928	0.00123158
$540$	−0.332412	−0.0143047
$541$	−28.7768	−1.23721	−0.618606	−	0.785701i	$-0.712302\pi$
$541$	−28.7768	−1.23721	−0.618606	+	0.785701i	$0.712302\pi$
$542$	−18.8911	−0.811442
$543$	9.03742	0.387833
$544$	3.25767	0.139672
$545$	−1.95394	−0.0836975
$546$	6.71179	0.287238
$547$	38.9013	1.66330	0.831649	−	0.555301i	$-0.187397\pi$
$547$	38.9013	1.66330	0.831649	+	0.555301i	$0.187397\pi$
$548$	−2.87652	−0.122879
$549$	7.83638	0.334449
$550$	−0.139805	−0.00596129
$551$	0.171799	0.00731886
$552$	−0.0708508	−0.00301561
$553$	4.61799	0.196377
$554$	15.3467	0.652019
$555$	−2.87265	−0.121937
$556$	13.4317	0.569630
$557$	10.5707	0.447894	0.223947	−	0.974601i	$-0.428106\pi$
$557$	10.5707	0.447894	0.223947	+	0.974601i	$0.428106\pi$
$558$	2.85299	0.120777
$559$	25.6407	1.08449
$560$	0.332412	0.0140470
$561$	−0.0931460	−0.00393263
$562$	18.2141	0.768315
$563$	−0.268622	−0.0113211	−0.00566053	−	0.999984i	$-0.501802\pi$
$563$	−0.268622	−0.0113211	−0.00566053	+	0.999984i	$0.501802\pi$
$564$	−3.20066	−0.134772
$565$	−0.863844	−0.0363422
$566$	23.9737	1.00769
$567$	1.00000	0.0419961
$568$	−11.2652	−0.472678
$569$	14.9638	0.627313	0.313657	−	0.949537i	$-0.398446\pi$
$569$	14.9638	0.627313	0.313657	+	0.949537i	$0.398446\pi$
$570$	−0.574600	−0.0240674
$571$	−29.2990	−1.22612	−0.613062	−	0.790035i	$-0.710062\pi$
$571$	−29.2990	−1.22612	−0.613062	+	0.790035i	$0.710062\pi$
$572$	−0.191909	−0.00802412
$573$	−1.00000	−0.0417756
$574$	0.999152	0.0417038
$575$	−0.346425	−0.0144469
$576$	1.00000	0.0416667
$577$	37.8934	1.57752	0.788760	−	0.614701i	$-0.210723\pi$
$577$	37.8934	1.57752	0.788760	+	0.614701i	$0.210723\pi$
$578$	−6.38757	−0.265688
$579$	12.2412	0.508727
$580$	0.0330374	0.00137180
$581$	−16.2076	−0.672404
$582$	−12.9496	−0.536779
$583$	−0.0989292	−0.00409723
$584$	12.8636	0.532299
$585$	−2.23108	−0.0922437
$586$	23.5020	0.970858
$587$	29.6902	1.22544	0.612722	−	0.790298i	$-0.290075\pi$
$587$	29.6902	1.22544	0.612722	+	0.790298i	$0.290075\pi$
$588$	−1.00000	−0.0412393
$589$	4.93163	0.203204
$590$	1.95791	0.0806061
$591$	−17.6606	−0.726459
$592$	8.64185	0.355178
$593$	39.6856	1.62969	0.814846	−	0.579677i	$-0.196821\pi$
$593$	39.6856	1.62969	0.814846	+	0.579677i	$0.196821\pi$
$594$	−0.0285928	−0.00117318
$595$	1.08289	0.0443941
$596$	0.853602	0.0349649
$597$	−1.97046	−0.0806454
$598$	−0.475536	−0.0194461
$599$	7.56812	0.309225	0.154612	−	0.987975i	$-0.450587\pi$
$599$	7.56812	0.309225	0.154612	+	0.987975i	$0.450587\pi$
$600$	4.88950	0.199613
$601$	32.4595	1.32405	0.662026	−	0.749481i	$-0.269697\pi$
$601$	32.4595	1.32405	0.662026	+	0.749481i	$0.269697\pi$
$602$	−3.82024	−0.155702
$603$	−0.0586398	−0.00238800
$604$	1.26304	0.0513923
$605$	−3.65626	−0.148648
$606$	−2.25647	−0.0916627
$607$	−2.23864	−0.0908634	−0.0454317	−	0.998967i	$-0.514466\pi$
$607$	−2.23864	−0.0908634	−0.0454317	+	0.998967i	$0.514466\pi$
$608$	1.72858	0.0701032
$609$	−0.0993871	−0.00402737
$610$	2.60490	0.105470
$611$	−21.4821	−0.869075
$612$	3.25767	0.131684
$613$	0.478264	0.0193169	0.00965845	−	0.999953i	$-0.496926\pi$
$613$	0.478264	0.0193169	0.00965845	+	0.999953i	$0.496926\pi$
$614$	−14.2852	−0.576502
$615$	−0.332130	−0.0133928
$616$	0.0285928	0.00115204
$617$	−18.1361	−0.730133	−0.365067	−	0.930981i	$-0.618954\pi$
$617$	−18.1361	−0.730133	−0.365067	+	0.930981i	$0.618954\pi$
$618$	−18.4861	−0.743622
$619$	−12.5204	−0.503237	−0.251619	−	0.967826i	$-0.580963\pi$
$619$	−12.5204	−0.503237	−0.251619	+	0.967826i	$0.580963\pi$
$620$	0.948367	0.0380874
$621$	−0.0708508	−0.00284314
$622$	21.0368	0.843499
$623$	16.0736	0.643975
$624$	6.71179	0.268687
$625$	23.3547	0.934190
$626$	−13.3859	−0.535008
$627$	−0.0494250	−0.00197384
$628$	−8.32618	−0.332251
$629$	28.1523	1.12251
$630$	0.332412	0.0132436
$631$	24.2059	0.963620	0.481810	−	0.876276i	$-0.339980\pi$
$631$	24.2059	0.963620	0.481810	+	0.876276i	$0.339980\pi$
$632$	4.61799	0.183694
$633$	25.3536	1.00771
$634$	16.9767	0.674230
$635$	4.60301	0.182665
$636$	3.45994	0.137195
$637$	−6.71179	−0.265931
$638$	0.00284175	0.000112506 0
$639$	−11.2652	−0.445645
$640$	0.332412	0.0131397
$641$	33.5226	1.32406	0.662031	−	0.749477i	$-0.269695\pi$
$641$	33.5226	1.32406	0.662031	+	0.749477i	$0.269695\pi$
$642$	−13.7691	−0.543424
$643$	20.4401	0.806078	0.403039	−	0.915183i	$-0.367954\pi$
$643$	20.4401	0.806078	0.403039	+	0.915183i	$0.367954\pi$
$644$	0.0708508	0.00279191
$645$	1.26989	0.0500020
$646$	5.63115	0.221555
$647$	−39.2127	−1.54161	−0.770806	−	0.637070i	$-0.780146\pi$
$647$	−39.2127	−1.54161	−0.770806	+	0.637070i	$0.780146\pi$
$648$	1.00000	0.0392837
$649$	0.168413	0.00661077
$650$	32.8173	1.28720
$651$	−2.85299	−0.111818
$652$	−1.32359	−0.0518359
$653$	12.9214	0.505652	0.252826	−	0.967512i	$-0.418640\pi$
$653$	12.9214	0.505652	0.252826	+	0.967512i	$0.418640\pi$
$654$	5.87807	0.229851
$655$	3.21773	0.125727
$656$	0.999152	0.0390103
$657$	12.8636	0.501856
$658$	3.20066	0.124775
$659$	19.0706	0.742886	0.371443	−	0.928456i	$-0.378863\pi$
$659$	19.0706	0.742886	0.371443	+	0.928456i	$0.378863\pi$
$660$	−0.00950458	−0.000369965 0
$661$	−40.6691	−1.58185	−0.790923	−	0.611915i	$-0.790399\pi$
$661$	−40.6691	−1.58185	−0.790923	+	0.611915i	$0.790399\pi$
$662$	31.3477	1.21836
$663$	21.8648	0.849160
$664$	−16.2076	−0.628976
$665$	0.574600	0.0222820
$666$	8.64185	0.334865
$667$	0.00704165	0.000272654 0
$668$	6.48446	0.250891
$669$	1.68373	0.0650966
$670$	−0.0194925	−0.000753063 0
$671$	0.224064	0.00864990
$672$	−1.00000	−0.0385758
$673$	−4.35009	−0.167684	−0.0838418	−	0.996479i	$-0.526719\pi$
$673$	−4.35009	−0.167684	−0.0838418	+	0.996479i	$0.526719\pi$
$674$	−17.3575	−0.668587
$675$	4.88950	0.188197
$676$	32.0482	1.23262
$677$	−34.7311	−1.33483	−0.667413	−	0.744688i	$-0.732598\pi$
$677$	−34.7311	−1.33483	−0.667413	+	0.744688i	$0.732598\pi$
$678$	2.59872	0.0998032
$679$	12.9496	0.496961
$680$	1.08289	0.0415269
$681$	7.47432	0.286416
$682$	0.0815750	0.00312367
$683$	2.18765	0.0837083	0.0418541	−	0.999124i	$-0.486674\pi$
$683$	2.18765	0.0837083	0.0418541	+	0.999124i	$0.486674\pi$
$684$	1.72858	0.0660939
$685$	−0.956188	−0.0365341
$686$	1.00000	0.0381802
$687$	−10.3911	−0.396447
$688$	−3.82024	−0.145645
$689$	23.2224	0.884702
$690$	−0.0235516	−0.000896595 0
$691$	4.72343	0.179688	0.0898438	−	0.995956i	$-0.471363\pi$
$691$	4.72343	0.179688	0.0898438	+	0.995956i	$0.471363\pi$
$692$	−0.314802	−0.0119670
$693$	0.0285928	0.00108615
$694$	26.6171	1.01037
$695$	4.46485	0.169361
$696$	−0.0993871	−0.00376726
$697$	3.25491	0.123289
$698$	−22.5782	−0.854597
$699$	−16.1566	−0.611100
$700$	−4.88950	−0.184806
$701$	−28.9583	−1.09374	−0.546870	−	0.837218i	$-0.684181\pi$
$701$	−28.9583	−1.09374	−0.546870	+	0.837218i	$0.684181\pi$
$702$	6.71179	0.253320
$703$	14.9381	0.563402
$704$	0.0285928	0.00107763
$705$	−1.06394	−0.0400701
$706$	0.854762	0.0321694
$707$	2.25647	0.0848632
$708$	−5.89003	−0.221361
$709$	−30.4003	−1.14171	−0.570854	−	0.821051i	$-0.693388\pi$
$709$	−30.4003	−1.14171	−0.570854	+	0.821051i	$0.693388\pi$
$710$	−3.74469	−0.140536
$711$	4.61799	0.173188
$712$	16.0736	0.602383
$713$	0.202137	0.00757008
$714$	−3.25767	−0.121915
$715$	−0.0637928	−0.00238571
$716$	−25.0999	−0.938026
$717$	5.75416	0.214893
$718$	15.4986	0.578401
$719$	1.17990	0.0440027	0.0220014	−	0.999758i	$-0.492996\pi$
$719$	1.17990	0.0440027	0.0220014	+	0.999758i	$0.492996\pi$
$720$	0.332412	0.0123882
$721$	18.4861	0.688460
$722$	−16.0120	−0.595905
$723$	−8.77669	−0.326409
$724$	−9.03742	−0.335873
$725$	−0.485953	−0.0180479
$726$	10.9992	0.408218
$727$	18.5237	0.687006	0.343503	−	0.939151i	$-0.388386\pi$
$727$	18.5237	0.687006	0.343503	+	0.939151i	$0.388386\pi$
$728$	−6.71179	−0.248756
$729$	1.00000	0.0370370
$730$	4.27600	0.158262
$731$	−12.4451	−0.460299
$732$	−7.83638	−0.289641
$733$	7.81516	0.288660	0.144330	−	0.989530i	$-0.453897\pi$
$733$	7.81516	0.288660	0.144330	+	0.989530i	$0.453897\pi$
$734$	24.6641	0.910369
$735$	−0.332412	−0.0122612
$736$	0.0708508	0.00261159
$737$	−0.00167668	−6.17612e−5 0
$738$	0.999152	0.0367793
$739$	13.1063	0.482124	0.241062	−	0.970510i	$-0.422504\pi$
$739$	13.1063	0.482124	0.241062	+	0.970510i	$0.422504\pi$
$740$	2.87265	0.105601
$741$	11.6019	0.426206
$742$	−3.45994	−0.127018
$743$	−11.2221	−0.411697	−0.205849	−	0.978584i	$-0.565995\pi$
$743$	−11.2221	−0.411697	−0.205849	+	0.978584i	$0.565995\pi$
$744$	−2.85299	−0.104596
$745$	0.283747	0.0103957
$746$	−19.5924	−0.717328
$747$	−16.2076	−0.593005
$748$	0.0931460	0.00340575
$749$	13.7691	0.503113
$750$	3.28739	0.120038
$751$	20.0766	0.732604	0.366302	−	0.930496i	$-0.380624\pi$
$751$	20.0766	0.732604	0.366302	+	0.930496i	$0.380624\pi$
$752$	3.20066	0.116716
$753$	1.70378	0.0620894
$754$	−0.667066	−0.0242931
$755$	0.419848	0.0152798
$756$	−1.00000	−0.0363696
$757$	3.38707	0.123105	0.0615526	−	0.998104i	$-0.480395\pi$
$757$	3.38707	0.123105	0.0615526	+	0.998104i	$0.480395\pi$
$758$	9.25494	0.336155
$759$	−0.00202582	−7.35327e−5 0
$760$	0.574600	0.0208429
$761$	−26.7232	−0.968716	−0.484358	−	0.874870i	$-0.660947\pi$
$761$	−26.7232	−0.968716	−0.484358	+	0.874870i	$0.660947\pi$
$762$	−13.8473	−0.501636
$763$	−5.87807	−0.212800
$764$	1.00000	0.0361787
$765$	1.08289	0.0391519
$766$	−11.8444	−0.427956
$767$	−39.5327	−1.42744
$768$	−1.00000	−0.0360844
$769$	−41.0287	−1.47953	−0.739766	−	0.672865i	$-0.765064\pi$
$769$	−41.0287	−1.47953	−0.739766	+	0.672865i	$0.765064\pi$
$770$	0.00950458	0.000342521 0
$771$	0.400063	0.0144079
$772$	−12.2412	−0.440570
$773$	20.0197	0.720057	0.360029	−	0.932941i	$-0.382767\pi$
$773$	20.0197	0.720057	0.360029	+	0.932941i	$0.382767\pi$
$774$	−3.82024	−0.137316
$775$	−13.9497	−0.501088
$776$	12.9496	0.464864
$777$	−8.64185	−0.310025
$778$	4.22403	0.151439
$779$	1.72712	0.0618803
$780$	2.23108	0.0798854
$781$	−0.322104	−0.0115258
$782$	0.230809	0.00825370
$783$	−0.0993871	−0.00355180
$784$	1.00000	0.0357143
$785$	−2.76772	−0.0987842
$786$	−9.67996	−0.345273
$787$	−2.10426	−0.0750087	−0.0375043	−	0.999296i	$-0.511941\pi$
$787$	−2.10426	−0.0750087	−0.0375043	+	0.999296i	$0.511941\pi$
$788$	17.6606	0.629132
$789$	−5.86895	−0.208940
$790$	1.53507	0.0546155
$791$	−2.59872	−0.0923998
$792$	0.0285928	0.00101600
$793$	−52.5962	−1.86775
$794$	30.1111	1.06860
$795$	1.15012	0.0407906
$796$	1.97046	0.0698409
$797$	−33.5109	−1.18702	−0.593508	−	0.804828i	$-0.702258\pi$
$797$	−33.5109	−1.18702	−0.593508	+	0.804828i	$0.702258\pi$
$798$	−1.72858	−0.0611911
$799$	10.4267	0.368870
$800$	−4.88950	−0.172870
$801$	16.0736	0.567932
$802$	5.72585	0.202187
$803$	0.367806	0.0129796
$804$	0.0586398	0.00206807
$805$	0.0235516	0.000830085 0
$806$	−19.1487	−0.674484
$807$	1.35497	0.0476973
$808$	2.25647	0.0793823
$809$	−3.05893	−0.107546	−0.0537731	−	0.998553i	$-0.517125\pi$
$809$	−3.05893	−0.107546	−0.0537731	+	0.998553i	$0.517125\pi$
$810$	0.332412	0.0116798
$811$	−27.2925	−0.958370	−0.479185	−	0.877714i	$-0.659068\pi$
$811$	−27.2925	−0.958370	−0.479185	+	0.877714i	$0.659068\pi$
$812$	0.0993871	0.00348780
$813$	18.8911	0.662540
$814$	0.247095	0.00866066
$815$	−0.439978	−0.0154118
$816$	−3.25767	−0.114041
$817$	−6.60360	−0.231031
$818$	−14.8710	−0.519954
$819$	−6.71179	−0.234529
$820$	0.332130	0.0115985
$821$	−32.2433	−1.12530	−0.562650	−	0.826695i	$-0.690218\pi$
$821$	−32.2433	−1.12530	−0.562650	+	0.826695i	$0.690218\pi$
$822$	2.87652	0.100330
$823$	19.9425	0.695153	0.347576	−	0.937652i	$-0.387005\pi$
$823$	19.9425	0.695153	0.347576	+	0.937652i	$0.387005\pi$
$824$	18.4861	0.643995
$825$	0.139805	0.00486737
$826$	5.89003	0.204940
$827$	−21.6304	−0.752161	−0.376081	−	0.926587i	$-0.622728\pi$
$827$	−21.6304	−0.752161	−0.376081	+	0.926587i	$0.622728\pi$
$828$	0.0708508	0.00246223
$829$	−19.1535	−0.665227	−0.332613	−	0.943063i	$-0.607930\pi$
$829$	−19.1535	−0.665227	−0.332613	+	0.943063i	$0.607930\pi$
$830$	−5.38759	−0.187006
$831$	−15.3467	−0.532371
$832$	−6.71179	−0.232690
$833$	3.25767	0.112872
$834$	−13.4317	−0.465101
$835$	2.15551	0.0745944
$836$	0.0494250	0.00170940
$837$	−2.85299	−0.0986138
$838$	28.9697	1.00074
$839$	−11.1550	−0.385115	−0.192557	−	0.981286i	$-0.561678\pi$
$839$	−11.1550	−0.385115	−0.192557	+	0.981286i	$0.561678\pi$
$840$	−0.332412	−0.0114693
$841$	−28.9901	−0.999659
$842$	−5.98538	−0.206270
$843$	−18.2141	−0.627327
$844$	−25.3536	−0.872706
$845$	10.6532	0.366481
$846$	3.20066	0.110041
$847$	−10.9992	−0.377936
$848$	−3.45994	−0.118815
$849$	−23.9737	−0.822775
$850$	−15.9284	−0.546340
$851$	0.612281	0.0209887
$852$	11.2652	0.385940
$853$	0.122498	0.00419426	0.00209713	−	0.999998i	$-0.499332\pi$
$853$	0.122498	0.00419426	0.00209713	+	0.999998i	$0.499332\pi$
$854$	7.83638	0.268156
$855$	0.574600	0.0196509
$856$	13.7691	0.470619
$857$	17.3276	0.591899	0.295950	−	0.955204i	$-0.404364\pi$
$857$	17.3276	0.591899	0.295950	+	0.955204i	$0.404364\pi$
$858$	0.191909	0.00655167
$859$	14.7259	0.502441	0.251221	−	0.967930i	$-0.419168\pi$
$859$	14.7259	0.502441	0.251221	+	0.967930i	$0.419168\pi$
$860$	−1.26989	−0.0433030
$861$	−0.999152	−0.0340510
$862$	28.8160	0.981478
$863$	−27.8870	−0.949286	−0.474643	−	0.880178i	$-0.657423\pi$
$863$	−27.8870	−0.949286	−0.474643	+	0.880178i	$0.657423\pi$
$864$	−1.00000	−0.0340207
$865$	−0.104644	−0.00355800
$866$	−25.4284	−0.864093
$867$	6.38757	0.216933
$868$	2.85299	0.0968369
$869$	0.132041	0.00447919
$870$	−0.0330374	−0.00112007
$871$	0.393578	0.0133359
$872$	−5.87807	−0.199056
$873$	12.9496	0.438278
$874$	0.122471	0.00414265
$875$	−3.28739	−0.111134
$876$	−12.8636	−0.434620
$877$	−3.65026	−0.123261	−0.0616303	−	0.998099i	$-0.519630\pi$
$877$	−3.65026	−0.123261	−0.0616303	+	0.998099i	$0.519630\pi$
$878$	−22.0601	−0.744492
$879$	−23.5020	−0.792703
$880$	0.00950458	0.000320399 0
$881$	−5.22841	−0.176149	−0.0880747	−	0.996114i	$-0.528071\pi$
$881$	−5.22841	−0.176149	−0.0880747	+	0.996114i	$0.528071\pi$
$882$	1.00000	0.0336718
$883$	−25.3127	−0.851839	−0.425919	−	0.904761i	$-0.640049\pi$
$883$	−25.3127	−0.851839	−0.425919	+	0.904761i	$0.640049\pi$
$884$	−21.8648	−0.735394
$885$	−1.95791	−0.0658146
$886$	13.5435	0.455004
$887$	−11.6777	−0.392098	−0.196049	−	0.980594i	$-0.562811\pi$
$887$	−11.6777	−0.392098	−0.196049	+	0.980594i	$0.562811\pi$
$888$	−8.64185	−0.290001
$889$	13.8473	0.464424
$890$	5.34305	0.179099
$891$	0.0285928	0.000957895 0
$892$	−1.68373	−0.0563753
$893$	5.53259	0.185141
$894$	−0.853602	−0.0285487
$895$	−8.34348	−0.278892
$896$	1.00000	0.0334077
$897$	0.475536	0.0158777
$898$	32.1764	1.07374
$899$	0.283550	0.00945694
$900$	−4.88950	−0.162983
$901$	−11.2713	−0.375503
$902$	0.0285686	0.000951229 0
$903$	3.82024	0.127130
$904$	−2.59872	−0.0864321
$905$	−3.00414	−0.0998611
$906$	−1.26304	−0.0419616
$907$	−48.1987	−1.60041	−0.800206	−	0.599725i	$-0.795277\pi$
$907$	−48.1987	−1.60041	−0.800206	+	0.599725i	$0.795277\pi$
$908$	−7.47432	−0.248044
$909$	2.25647	0.0748423
$910$	−2.23108	−0.0739595
$911$	24.7602	0.820341	0.410170	−	0.912009i	$-0.365469\pi$
$911$	24.7602	0.820341	0.410170	+	0.912009i	$0.365469\pi$
$912$	−1.72858	−0.0572390
$913$	−0.463420	−0.0153370
$914$	−36.9368	−1.22176
$915$	−2.60490	−0.0861155
$916$	10.3911	0.343333
$917$	9.67996	0.319661
$918$	−3.25767	−0.107519
$919$	17.6478	0.582147	0.291074	−	0.956701i	$-0.405988\pi$
$919$	17.6478	0.582147	0.291074	+	0.956701i	$0.405988\pi$
$920$	0.0235516	0.000776474 0
$921$	14.2852	0.470712
$922$	−30.9432	−1.01906
$923$	75.6099	2.48873
$924$	−0.0285928	−0.000940634 0
$925$	−42.2543	−1.38931
$926$	−15.4331	−0.507162
$927$	18.4861	0.607165
$928$	0.0993871	0.00326254
$929$	12.1478	0.398557	0.199279	−	0.979943i	$-0.436140\pi$
$929$	12.1478	0.398557	0.199279	+	0.979943i	$0.436140\pi$
$930$	−0.948367	−0.0310982
$931$	1.72858	0.0566519
$932$	16.1566	0.529228
$933$	−21.0368	−0.688714
$934$	7.14773	0.233881
$935$	0.0309628	0.00101259
$936$	−6.71179	−0.219382
$937$	−8.00653	−0.261562	−0.130781	−	0.991411i	$-0.541748\pi$
$937$	−8.00653	−0.261562	−0.130781	+	0.991411i	$0.541748\pi$
$938$	−0.0586398	−0.00191466
$939$	13.3859	0.436832
$940$	1.06394	0.0347017
$941$	57.5833	1.87716	0.938580	−	0.345061i	$-0.112142\pi$
$941$	57.5833	1.87716	0.938580	+	0.345061i	$0.112142\pi$
$942$	8.32618	0.271282
$943$	0.0707907	0.00230526
$944$	5.89003	0.191704
$945$	−0.332412	−0.0108133
$946$	−0.109231	−0.00355142
$947$	−51.5809	−1.67615	−0.838076	−	0.545553i	$-0.816320\pi$
$947$	−51.5809	−1.67615	−0.838076	+	0.545553i	$0.816320\pi$
$948$	−4.61799	−0.149985
$949$	−86.3377	−2.80264
$950$	−8.45190	−0.274216
$951$	−16.9767	−0.550506
$952$	3.25767	0.105582
$953$	−32.7561	−1.06107	−0.530537	−	0.847662i	$-0.678010\pi$
$953$	−32.7561	−1.06107	−0.530537	+	0.847662i	$0.678010\pi$
$954$	−3.45994	−0.112020
$955$	0.332412	0.0107566
$956$	−5.75416	−0.186103
$957$	−0.00284175	−9.18609e−5 0
$958$	22.1217	0.714719
$959$	−2.87652	−0.0928876
$960$	−0.332412	−0.0107285
$961$	−22.8604	−0.737433
$962$	−58.0023	−1.87007
$963$	13.7691	0.443704
$964$	8.77669	0.282678
$965$	−4.06912	−0.130989
$966$	−0.0708508	−0.00227959
$967$	22.5973	0.726679	0.363339	−	0.931657i	$-0.381637\pi$
$967$	22.5973	0.726679	0.363339	+	0.931657i	$0.381637\pi$
$968$	−10.9992	−0.353527
$969$	−5.63115	−0.180899
$970$	4.30460	0.138212
$971$	−37.9951	−1.21932	−0.609660	−	0.792663i	$-0.708694\pi$
$971$	−37.9951	−1.21932	−0.609660	+	0.792663i	$0.708694\pi$
$972$	−1.00000	−0.0320750
$973$	13.4317	0.430600
$974$	2.26919	0.0727096
$975$	−32.8173	−1.05100
$976$	7.83638	0.250837
$977$	−38.2839	−1.22481	−0.612405	−	0.790544i	$-0.709798\pi$
$977$	−38.2839	−1.22481	−0.612405	+	0.790544i	$0.709798\pi$
$978$	1.32359	0.0423239
$979$	0.459589	0.0146885
$980$	0.332412	0.0106185
$981$	−5.87807	−0.187672
$982$	−41.7450	−1.33214
$983$	−46.8923	−1.49563	−0.747816	−	0.663906i	$-0.768897\pi$
$983$	−46.8923	−1.49563	−0.747816	+	0.663906i	$0.768897\pi$
$984$	−0.999152	−0.0318518
$985$	5.87058	0.187052
$986$	0.323771	0.0103110
$987$	−3.20066	−0.101878
$988$	−11.6019	−0.369105
$989$	−0.270667	−0.00860672
$990$	0.00950458	0.000302075 0
$991$	−23.7080	−0.753109	−0.376555	−	0.926394i	$-0.622891\pi$
$991$	−23.7080	−0.753109	−0.376555	+	0.926394i	$0.622891\pi$
$992$	2.85299	0.0905826
$993$	−31.3477	−0.994788
$994$	−11.2652	−0.357311
$995$	0.655002	0.0207650
$996$	16.2076	0.513557
$997$	4.53237	0.143542	0.0717708	−	0.997421i	$-0.477135\pi$
$997$	4.53237	0.143542	0.0717708	+	0.997421i	$0.477135\pi$
$998$	−0.872781	−0.0276274
$999$	−8.64185	−0.273416

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8022.2.a.r.1.5	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8022.2.a.r.1.5	✓	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8022 = 2 \cdot 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.332412 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.332412 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.332412 q^{10} +0.0285928 q^{11} -1.00000 q^{12} -6.71179 q^{13} +1.00000 q^{14} -0.332412 q^{15} +1.00000 q^{16} +3.25767 q^{17} +1.00000 q^{18} +1.72858 q^{19} +0.332412 q^{20} -1.00000 q^{21} +0.0285928 q^{22} +0.0708508 q^{23} -1.00000 q^{24} -4.88950 q^{25} -6.71179 q^{26} -1.00000 q^{27} +1.00000 q^{28} +0.0993871 q^{29} -0.332412 q^{30} +2.85299 q^{31} +1.00000 q^{32} -0.0285928 q^{33} +3.25767 q^{34} +0.332412 q^{35} +1.00000 q^{36} +8.64185 q^{37} +1.72858 q^{38} +6.71179 q^{39} +0.332412 q^{40} +0.999152 q^{41} -1.00000 q^{42} -3.82024 q^{43} +0.0285928 q^{44} +0.332412 q^{45} +0.0708508 q^{46} +3.20066 q^{47} -1.00000 q^{48} +1.00000 q^{49} -4.88950 q^{50} -3.25767 q^{51} -6.71179 q^{52} -3.45994 q^{53} -1.00000 q^{54} +0.00950458 q^{55} +1.00000 q^{56} -1.72858 q^{57} +0.0993871 q^{58} +5.89003 q^{59} -0.332412 q^{60} +7.83638 q^{61} +2.85299 q^{62} +1.00000 q^{63} +1.00000 q^{64} -2.23108 q^{65} -0.0285928 q^{66} -0.0586398 q^{67} +3.25767 q^{68} -0.0708508 q^{69} +0.332412 q^{70} -11.2652 q^{71} +1.00000 q^{72} +12.8636 q^{73} +8.64185 q^{74} +4.88950 q^{75} +1.72858 q^{76} +0.0285928 q^{77} +6.71179 q^{78} +4.61799 q^{79} +0.332412 q^{80} +1.00000 q^{81} +0.999152 q^{82} -16.2076 q^{83} -1.00000 q^{84} +1.08289 q^{85} -3.82024 q^{86} -0.0993871 q^{87} +0.0285928 q^{88} +16.0736 q^{89} +0.332412 q^{90} -6.71179 q^{91} +0.0708508 q^{92} -2.85299 q^{93} +3.20066 q^{94} +0.574600 q^{95} -1.00000 q^{96} +12.9496 q^{97} +1.00000 q^{98} +0.0285928 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} - 10 q^{3} + 10 q^{4} + 8 q^{5} - 10 q^{6} + 10 q^{7} + 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 - 10 * q^3 + 10 * q^4 + 8 * q^5 - 10 * q^6 + 10 * q^7 + 10 * q^8 + 10 * q^9	\( 10 q + 10 q^{2} - 10 q^{3} + 10 q^{4} + 8 q^{5} - 10 q^{6} + 10 q^{7} + 10 q^{8} + 10 q^{9} + 8 q^{10} + 4 q^{11} - 10 q^{12} + 6 q^{13} + 10 q^{14} - 8 q^{15} + 10 q^{16} + 5 q^{17} + 10 q^{18} + 15 q^{19} + 8 q^{20} - 10 q^{21} + 4 q^{22} + 12 q^{23} - 10 q^{24} - 2 q^{25} + 6 q^{26} - 10 q^{27} + 10 q^{28} + 7 q^{29} - 8 q^{30} + 28 q^{31} + 10 q^{32} - 4 q^{33} + 5 q^{34} + 8 q^{35} + 10 q^{36} - 3 q^{37} + 15 q^{38} - 6 q^{39} + 8 q^{40} + 24 q^{41} - 10 q^{42} + 4 q^{43} + 4 q^{44} + 8 q^{45} + 12 q^{46} + 16 q^{47} - 10 q^{48} + 10 q^{49} - 2 q^{50} - 5 q^{51} + 6 q^{52} + 5 q^{53} - 10 q^{54} - q^{55} + 10 q^{56} - 15 q^{57} + 7 q^{58} + 17 q^{59} - 8 q^{60} + 15 q^{61} + 28 q^{62} + 10 q^{63} + 10 q^{64} + 14 q^{65} - 4 q^{66} + 6 q^{67} + 5 q^{68} - 12 q^{69} + 8 q^{70} + 5 q^{71} + 10 q^{72} + 16 q^{73} - 3 q^{74} + 2 q^{75} + 15 q^{76} + 4 q^{77} - 6 q^{78} - 5 q^{79} + 8 q^{80} + 10 q^{81} + 24 q^{82} + 24 q^{83} - 10 q^{84} - 19 q^{85} + 4 q^{86} - 7 q^{87} + 4 q^{88} + 17 q^{89} + 8 q^{90} + 6 q^{91} + 12 q^{92} - 28 q^{93} + 16 q^{94} + 15 q^{95} - 10 q^{96} + 20 q^{97} + 10 q^{98} + 4 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 - 10 * q^3 + 10 * q^4 + 8 * q^5 - 10 * q^6 + 10 * q^7 + 10 * q^8 + 10 * q^9 + 8 * q^10 + 4 * q^11 - 10 * q^12 + 6 * q^13 + 10 * q^14 - 8 * q^15 + 10 * q^16 + 5 * q^17 + 10 * q^18 + 15 * q^19 + 8 * q^20 - 10 * q^21 + 4 * q^22 + 12 * q^23 - 10 * q^24 - 2 * q^25 + 6 * q^26 - 10 * q^27 + 10 * q^28 + 7 * q^29 - 8 * q^30 + 28 * q^31 + 10 * q^32 - 4 * q^33 + 5 * q^34 + 8 * q^35 + 10 * q^36 - 3 * q^37 + 15 * q^38 - 6 * q^39 + 8 * q^40 + 24 * q^41 - 10 * q^42 + 4 * q^43 + 4 * q^44 + 8 * q^45 + 12 * q^46 + 16 * q^47 - 10 * q^48 + 10 * q^49 - 2 * q^50 - 5 * q^51 + 6 * q^52 + 5 * q^53 - 10 * q^54 - q^55 + 10 * q^56 - 15 * q^57 + 7 * q^58 + 17 * q^59 - 8 * q^60 + 15 * q^61 + 28 * q^62 + 10 * q^63 + 10 * q^64 + 14 * q^65 - 4 * q^66 + 6 * q^67 + 5 * q^68 - 12 * q^69 + 8 * q^70 + 5 * q^71 + 10 * q^72 + 16 * q^73 - 3 * q^74 + 2 * q^75 + 15 * q^76 + 4 * q^77 - 6 * q^78 - 5 * q^79 + 8 * q^80 + 10 * q^81 + 24 * q^82 + 24 * q^83 - 10 * q^84 - 19 * q^85 + 4 * q^86 - 7 * q^87 + 4 * q^88 + 17 * q^89 + 8 * q^90 + 6 * q^91 + 12 * q^92 - 28 * q^93 + 16 * q^94 + 15 * q^95 - 10 * q^96 + 20 * q^97 + 10 * q^98 + 4 * q^99

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